How to get MacOS Montenry in MacBook Pro(15inch 2016), While App Store don't show the software update

Monterey is compatible with the OP's 2016 MacBookPro. He/she only needs to download the installer per the instructions in How to download and install macOS - Apple Support

The App Store only shows the latest version of macOS (today that's Sonoma). It does not show "all versions compatible with your Mac." Monterey simply does not appear in the general App Store any more and search will not find it there.

See this article for instructions -> How to download and install macOS - Apple Support

The App Store only shows software that is compatible with your Mac. If macOS Monterey isn't appearing, it may not be compatible with your device.

However, there are success stories of installing Monterey on even older MacBooks (2015) by creating a bootable USB flash drive and going through a manual OS installation process.